An apparatus is known for the clamping of a component on a rotating machine part of a balancing machine from WO 00/45983 A1. The clamping apparatus disclosed there is designed for the centric clamping of tool holders, provided with a hollow shank taper, on a balancing machine. The clamping device contains for this purpose a basic body with a conical holder opening into which the hollow shaft taper of the tool holder to be clamped is inserted. A clamping collet with radially movable collet elements is located within the basic body; it can move by means of an axially movable inner clamping mandrel between a radial inner release position and a radial outer clamping position. The collet elements serving as the clamping device are designed in such a way that, in the clamping position, they mesh into an inner annular groove in the hollow shaft taper and pull it, in the axial direction, into the conical holder opening of the basic body. The tool holder is centered by the axial pulling of the hollow shaft taper into the corresponding conical holder opening of the basic body.